Is there a function, or combination of nested functions to count the number
of zeros in a row up until the first non-zero valued cell?

For Example

0 0 0 0 0 35 0 50 60
0 0 0 0 0 0 40 10 0 0 30

For the First Row I want the function to return the value 6 and the second
row to return the value '7'

I do not want to know the total number of zeros in a row, I want to know the
number of zeros in a row until I encounter the first nonzero cell.